Biconservative quasi-minimal immersions into semi-Euclidean spaces

Abstract

In this paper we study biconservative immersions into the semi-Riemannian space form $R_2^4(c)$ of dimension 4, index 2 and constant curvature, where $c\in \{0,-1,1\}$. First, we obtain a characterization of quasi-minimal proper biconservative immersions into $R_2^4(c)$. Then we obtain the complete classification of quasi-minimal biconservative surfaces in $R_2^4(0)={\mathbb{E}}_2^4$. We also obtain a new class of biharmonic quasi-minimal isometric immersion into ${\mathbb{E}}_2^4$.

This work was obtained during the ITU-GAP project \emph{ARI2Harmoni} (Project Number: TGA-2017-40722)

References in corpus (2)

• Biharmonic hypersurfaces with three distinct principal curvatures in Euclidean space
• Biconservative ideal hypersurfaces in Euclidean spaces